Optimal. Leaf size=61 \[ \frac{2 (x+1)^{3/2}}{105 (1-x)^{3/2}}+\frac{2 (x+1)^{3/2}}{35 (1-x)^{5/2}}+\frac{(x+1)^{3/2}}{7 (1-x)^{7/2}} \]
[Out]
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Rubi [A] time = 0.0367635, antiderivative size = 61, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{2 (x+1)^{3/2}}{105 (1-x)^{3/2}}+\frac{2 (x+1)^{3/2}}{35 (1-x)^{5/2}}+\frac{(x+1)^{3/2}}{7 (1-x)^{7/2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 + x]/(1 - x)^(9/2),x]
[Out]
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Rubi in Sympy [A] time = 5.69046, size = 48, normalized size = 0.79 \[ \frac{2 \left (x + 1\right )^{\frac{3}{2}}}{105 \left (- x + 1\right )^{\frac{3}{2}}} + \frac{2 \left (x + 1\right )^{\frac{3}{2}}}{35 \left (- x + 1\right )^{\frac{5}{2}}} + \frac{\left (x + 1\right )^{\frac{3}{2}}}{7 \left (- x + 1\right )^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)**(1/2)/(1-x)**(9/2),x)
[Out]
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Mathematica [A] time = 0.0186272, size = 35, normalized size = 0.57 \[ \frac{\sqrt{1-x^2} \left (2 x^3-8 x^2+13 x+23\right )}{105 (x-1)^4} \]
Warning: Unable to verify antiderivative.
[In] Integrate[Sqrt[1 + x]/(1 - x)^(9/2),x]
[Out]
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Maple [A] time = 0.004, size = 25, normalized size = 0.4 \[{\frac{2\,{x}^{2}-10\,x+23}{105} \left ( 1+x \right ) ^{{\frac{3}{2}}} \left ( 1-x \right ) ^{-{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)^(1/2)/(1-x)^(9/2),x)
[Out]
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Maxima [A] time = 1.3411, size = 128, normalized size = 2.1 \[ \frac{2 \, \sqrt{-x^{2} + 1}}{7 \,{\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}} + \frac{\sqrt{-x^{2} + 1}}{35 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} - \frac{2 \, \sqrt{-x^{2} + 1}}{105 \,{\left (x^{2} - 2 \, x + 1\right )}} + \frac{2 \, \sqrt{-x^{2} + 1}}{105 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)/(-x + 1)^(9/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203878, size = 204, normalized size = 3.34 \[ \frac{25 \, x^{7} - 14 \, x^{6} - 301 \, x^{5} + 700 \, x^{4} - 350 \, x^{3} - 840 \, x^{2} - 7 \,{\left (3 \, x^{6} - 23 \, x^{5} + 40 \, x^{4} + 10 \, x^{3} - 120 \, x^{2} + 120 \, x\right )} \sqrt{x + 1} \sqrt{-x + 1} + 840 \, x}{105 \,{\left (x^{7} - 14 \, x^{5} + 28 \, x^{4} - 7 \, x^{3} - 28 \, x^{2} -{\left (x^{6} - 7 \, x^{5} + 11 \, x^{4} + 7 \, x^{3} - 32 \, x^{2} + 28 \, x - 8\right )} \sqrt{x + 1} \sqrt{-x + 1} + 28 \, x - 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)/(-x + 1)^(9/2),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)**(1/2)/(1-x)**(9/2),x)
[Out]
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GIAC/XCAS [A] time = 0.210325, size = 39, normalized size = 0.64 \[ \frac{{\left (2 \,{\left (x + 1\right )}{\left (x - 6\right )} + 35\right )}{\left (x + 1\right )}^{\frac{3}{2}} \sqrt{-x + 1}}{105 \,{\left (x - 1\right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)/(-x + 1)^(9/2),x, algorithm="giac")
[Out]